640 Chapter 17
computer-based measurement system, processing and
display of the data can be accomplished at any time
after the raw data has been taken.
The effects of time windowing are present in any
signal measurement, since the measurement must be
initiated and completed in a finite amount of time
(window). In digital measurement systems, however,
the exact size of the time window, and therefore the
resultant tradeoffs in resolution, are more directly
controllable. There are two general approaches to
acquiring a loudspeaker’s transfer function via
time-windowed measurements: measurement of the
device’s impulse response (time-domain measurement)
or acquisition of the device’s transfer function in the
frequency domain.
17.11.4.1 Measurement of the Impulse Response
One form of input signal that is highly useful as an exci-
tation for test and analysis purposes is an impulse.
Mathematically, the signal is described by a Dirac delta
function. Descriptively, an impulse is a voltage “spike”
of very short duration and relatively large amplitude. An
interesting property of an impulse is that it contains all
frequencies at the same level. The impulse response of a
loudspeaker, via the Fourier transform (or fast Fourier
transform, FFT, as implemented in computer-based
instruments), gives the speaker’s transfer function. It is
this equivalency via transform of the impulse response
and transfer function that allows us to fully characterize
a two-port device through measurement taken in only
one domain or the other (time or frequency).
If a loudspeaker is excited with an impulse, the
signal from a suitably well-behaved test microphone
placed in front of the speaker will represent the loud-
speaker’s impulse response at that point. This signal
may be digitized and post processed to yield the
frequency-domain transfer function, as well as a number
of other functions. The sampling process takes place
over a fixed amount of time (the time window), and its
initiation may be delayed to remove the effect of time
required for sound to travel from the loudspeaker to the
test microphone (propagation delay). Additionally, the
length of the time window may be chosen so as to reject
reflections from the room in which the measurement is
being made. This is termed a quasianechoic measure-
ment, and its availability has made it possible to acquire
accurate direct-field response data on loudspeakers
without an anechoic chamber.
The mathematics of Fourier series requires that the
signal value be zero at the beginning and end of the time
window. Since this condition is not generally satisfied, a
window function is applied to the sampled data to force
the endpoints of the window to zero. The effect of the
window function is to create inaccuracies in the calcu-
lated transfer function, but these are generally much less
than the spectral inaccuracies that would result from
unwindowed (truncated) data. Various types of window
functions may be used, including square (equivalent to
unwindowed data), Gaussian, Hamming, and Hanning.
Each has its advantages and drawbacks.
Among the disadvantages of impulse excitation is
that of SNR. Because the impulse is of short duration,
quiescent noise in the test environment can easily
corrupt the test data. One means of reducing the effect
of background noise is to average the results of multiple
tests. If the noise is random, and therefore uncorrelated
with the test signal, each doubling of the number of
averages has the potential of reducing the relative noise
level by 3 dB. Averaging increases the amount of time
required to acquire the data.
Another disadvantage of impulse excitation is that it
provides no means of identifying nonlinearities (distor-
tion) in the loudspeaker. Distortion products appear no
differently to the analyzer than the linear portion of the
device’s response.17.11.4.2 Maximum Length Sequence MeasurementsA variation on the method of impulse excitation is
called maximum length sequence, or MLS, testing. In
this form of measurement, the excitation signal is a
series of pulses that repeats itself. The loudspeaker’s
impulse response is derived by calculating the
cross-correlation between the input and output signals.
This excitation signal has the advantage of producing
higher average signal levels than an impulse, therefore
improving the signal/noise performance of the test.
Additionally, the effects of certain types of distortion
can be reduced substantially by running a series of tests
employing a strategically chosen set of signal sequence
lengths. To be accurate, an MLS test must be configured
such that the duration of the signal sequence exceeds
the length of the impulse response of the device under
test. In the case of loudspeaker measurements, the
impulse response of the acoustic environment must be
accounted for in order to satisfy the requirement.17.11.4.3 Other FFT-Based MeasurementsYet another variation on the FFT technique is a type of
measurement that can use an arbitrary signal as the exci-
tation signal. This form of measurement is a
dual-channel FFT measurement, and the variations on